What happens to the magnitude of the force of gravitation between two objects if –
Mass of both objects as well as the distance between them is doubled ?
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2
It will not change, as if we double each object's mass,then the total increase in numerator will be 4 times the previous one, while doubling the distance will result in 4 times the distance of previous one [as numerator is divded by (distance)^2]
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F = Gm1m2/r².......(1)
where G = universal gravitational constant
m1 = mass of first object
m2 = mass of second object
r = distance between m1 and m2 in the line joining the centres.
Now, mass of both the objects and distance were doubled
F' = G(2m1)(2m2)/(2r)²
F' = 4 Gm1m2/4r²
F' = Gm1m2/r².....(2)
F = F'
It will remain same.
where G = universal gravitational constant
m1 = mass of first object
m2 = mass of second object
r = distance between m1 and m2 in the line joining the centres.
Now, mass of both the objects and distance were doubled
F' = G(2m1)(2m2)/(2r)²
F' = 4 Gm1m2/4r²
F' = Gm1m2/r².....(2)
F = F'
It will remain same.
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